An estimate for the distance of a complex valued Sobolev function defined on the unit disc to the class of holomorphic functions

Abstract

Let ƒ : B → ℂ denote a Sobolev function of class defined on the unit disc. We show that the distance of ƒ to the class of all holomorphic functions measured in the norm of the space is bounded by the Lp-norm of theWirtinger derivative . As a consequence we obtain a Korn type inequality for vector fields .